Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).


An electric bill is an essential expense for young people who get their first apartment. The following is a list of Jordan's monthly electric bills for the past 10 months.
$115, $150, $144, $126, $90, $90, $95, $110, $120, $88
Round your answers to the nearest cent.
a. What is the mean monthly electric bill? 
 
b. What is the range? 
 
c. What is the variance? 
456.76
 
d. What is the standard deviation? 

Let's solve each part of the problem step by step.

### Given Data:
Jordan's monthly electric bills for the past 10 months are:
\[
115, 150, 144, 126, 90, 90, 95, 110, 120, 88
\]

### a. Mean Monthly Electric Bill

The **mean** is calculated by summing all the bills and dividing by the number of months.

\[
\text{Mean} = \frac{115 + 150 + 144 + 126 + 90 + 90 + 95 + 110 + 120 + 88}{10}
\]
\[
\text{Mean} = \frac{1128}{10} = 112.80
\]

So, the mean monthly electric bill is **$112.80**.

### b. Range

The **range** is the difference between the highest and lowest bill.

\[
\text{Range} = 150 - 88 = 62
\]

So, the range of the electric bills is **$62**.

### c. Variance

The **variance** is calculated using the formula:

\[
\text{Variance} = \frac{1}{N} \sum_{i=1}^{N} (x_i - \text{Mean})^2
\]
Where $ N $ is the number of bills (10 in this case), and $ x_i $ is each bill.

1. Calculate the squared differences:
   \[
   (115 - 112.80)^2 = 4.84
   \]
   \[
   (150 - 112.80)^2 = 1379.84
   \]
   \[
   (144 - 112.80)^2 = 968.64
   \]
   \[
   (126 - 112.80)^2 = 173.44
   \]
   \[
   (90 - 112.80)^2 = 523.84
   \]
   \[
   (90 - 112.80)^2 = 523.84
   \]
   \[
   (95 - 112.80)^2 = 319.84
   \]
   \[
   (110 - 112.80)^2 = 7.84
   \]
   \[
   (120 - 112.80)^2 = 51.84
   \]
   \[
   (88 - 112.80)^2 = 620.64
   \]

2. Sum of squared differences:
   \[
   4.84 + 1379.84 + 968.64 + 173.44 + 523.84 + 523.84 + 319.84 + 7.84 + 51.84 + 620.64 = 4574.76
   \]

3. Divide by the number of bills to find the variance:
   \[
   \text{Variance} = \frac{4574.76}{10} = 457.48
   \]

So, the variance of the electric bills is **$457.48**.

### d. Standard Deviation

The **standard deviation** is the square root of the variance:

\[
\text{Standard Deviation} = \sqrt{457.48} \approx 21.39
\]

So, the standard deviation of the electric bills is **$21.39**.

---

If you have any questions or need further details, feel free to ask. Here are five related questions to consider:

1. How would the mean change if the highest bill was $160 instead of $150?
2. What impact would doubling all bills have on the variance and standard deviation?
3. How does the standard deviation help in understanding the variability of Jordan's electric bills?
4. What would the range be if the lowest bill was $80 instead of $88?
5. How would the variance change if we excluded the highest and lowest bills?

**Tip:** Understanding the variance and standard deviation helps in assessing the consistency of monthly expenses.

An electric bill is an essential expense for young people who get their first apartment. The following is a list of Jordan's monthly electric bills for the past 10 months. $115, $150, $144, $126, $90, $90, $95, $110, $120, $88 Round your answers to the nearest cent. a. What is the mean monthly electric bill? b. What is the range? c. What is the variance? d. What is the standard deviation?

Learn how to calculate the mean, range, variance, and standard deviation of Jordan's monthly electric bills. This problem covers key statistical concepts such as mean, range, variance, and standard deviation. Perfect for high school students in Grades 9-12.

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